Hybridizations of GRASP with path relinking for the far from most string problem

The traveling salesman problem (TSP) is one of the most studied problems in combinatorial optimization. Given a set of nodes and the distances between them, it consists in finding the shortest route that visits each node exactly once and returns to the first. Nevertheless, more flexible and applicable formulations of this problem exist and can be considered. The Steiner TSP (STSP) is a variant of the TSP that assumes that only a given subset of nodes must be visited by the shortest route, eventually visiting some nodes and edges more than once. In this paper, we adapt some classical TSP constructive heuristics and neighborhood structures to the STSP variant. In particular, we propose a reduced 2‐opt neighborhood and we show that it leads to better results in smaller computation times. Computational results with an implementation of a GRASP heuristic using path‐relinking and restarts are reported. In addition, ten large test instances are generated. All instances and their best‐known solutions are made available for download and benchmarking purposes.

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“…Annotated bibliographies of GRASP appeared in Resende (2009a, 2009b). A recent application of GRASP appeared in Ferone et al (2016).…”

Section: Grasp With Path-relinking Heuristicmentioning

confidence: 99%

A GRASP heuristic using path‐relinking and restarts for the Steiner traveling salesman problem

Interian

Ribeiro

2017

Int Trans Operational Res

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“…Furthermore, they declared that the combination of PR with SS gave the best results. Recently, in [26,27], path relinking is also hybridized with other heuristics showing good results. Based on these results, we were motivated for hybridizing this procedure within the evolutionary framework.…”

Section: A Hybrid Evolutionary Algorithm With Path Relinkingmentioning

confidence: 99%

Analyzing the Performance of a Hybrid Heuristic for Solving a Bilevel Location Problem under Different Approaches to Tackle the Lower Level

Maldonado-Pinto¹,

Casas-Ramírez

Camacho‐Vallejo³

2016

Mathematical Problems in Engineering

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The problem addressed here is a combinatorial bilevel programming problem called the uncapacitated facility location problem with customer’s preferences. A hybrid algorithm is developed for solving a battery of benchmark instances. The algorithm hybridizes an evolutionary algorithm with path relinking; the latter procedure is added into the crossover phase for exploring the trajectory between both parents. The proposed algorithm outperforms the evolutionary algorithm already existing in the literature. Results show that including a more sophisticated procedure for improving the population through the generations accelerates the convergence of the algorithm. In order to support the latter statement, a reduction of around the half of the computational time is obtained by using the hybrid algorithm. Moreover, due to the nature of bilevel problems, if feasible solutions are desired, then the lower level must be solved for each change in the upper level’s current solution. A study for illustrating the impact in the algorithm’s performance when solving the lower level through three different exact or heuristic approaches is made.

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“…The recent application in a hard combinatorial problem coming from biological systems, which can be found in Ferone et al. (). Here, we will develop a GRASP heuristic enriched with VND and a Shaking operation in order to prevent being trapped in local optima.…”

Section: Graspmentioning

confidence: 99%

“…GRASP has been successfully applied to several problems arising in telecommunications, such as optical systems (Duarte et al, 2014), WDM systems (Wu et al, 2015), and WAN design (Robledo Amoza, 2005), and many other fields of knowledge. The recent application in a hard combinatorial problem coming from biological systems, which can be found in Ferone et al (2016). Here, we will develop a GRASP heuristic enriched with VND and a Shaking operation in order to prevent being trapped in local optima.…”

Section: Graspmentioning

confidence: 99%

Two‐node‐connected star problem

Recoba

Robledo

Romero

et al. 2016

Int Trans Operational Res

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In this study, a two‐node‐connected star problem (2NCSP) is introduced. We are given a simple graph and internal and external costs for each link of the graph. The goal is to find the minimum‐cost spanning subgraph, where the core is two‐node‐connected and the remaining external nodes are connected to the core. First, we show that the 2NCSP belongs to the class of NP‐hard computational problems. Therefore, a greedy randomized adaptive search procedure (GRASP) heuristic is developed, enriched with a variable neighborhood descent (VND). The neighborhood structures include exact integer linear programming models to find the best paths and two‐node‐connected replacements, as well as a shaking operation in order to prevent being trapped in a local minima. The ring star problem (RSP) represents a relevant model in network optimization, where the core is a ring instead of an arbitrary two‐node‐connected graph. We contrast our GRASP/VND methodology with a previous reference work on the RSP in order to highlight the effectiveness of our heuristic. The heuristic is competitive, and the best results produced for several instances so far are under study. In this study, a discussion of the results and trends for future work are provided.

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Hybridizations of GRASP with path relinking for the far from most string problem

Cited by 15 publications

References 35 publications

A GRASP heuristic using path‐relinking and restarts for the Steiner traveling salesman problem

A GRASP heuristic using path‐relinking and restarts for the Steiner traveling salesman problem

Analyzing the Performance of a Hybrid Heuristic for Solving a Bilevel Location Problem under Different Approaches to Tackle the Lower Level

Two‐node‐connected star problem

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